Multicritical points of unitary matrix model with logarithmic potential identified with Argyres-Douglas points
| Autor: | Takeshi Oota, Katsuya Yano, Hiroshi Itoyama |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
High Energy Physics - Theory
Physics Nuclear and High Energy Physics Partition function (quantum field theory) Logarithm 010308 nuclear & particles physics FOS: Physical sciences Astronomy and Astrophysics Supersymmetry Unitary matrix Function (mathematics) 01 natural sciences Atomic and Molecular Physics and Optics Term (time) High Energy Physics - Theory (hep-th) 0103 physical sciences 010306 general physics Mathematical physics |
| DOI: | 10.48550/arxiv.1909.10770 |
| Popis: | In [arXiv:1805.05057 [hep-th]],[arXiv:1812.00811 [hep-th]], the partition function of the Gross-Witten-Wadia unitary matrix model with the logarithmic term has been identified with the $\tau$ function of a certain Painlev\'{e} system, and the double scaling limit of the associated discrete Painlev\'{e} equation to the critical point provides us with the Painlev\'{e} II equation. This limit captures the critical behavior of the $su(2)$, $N_f =2$ $\mathcal{N}=2$ supersymmetric gauge theory around its Argyres-Douglas $4D$ superconformal point. Here, we consider further extension of the model that contains the $k$-th multicritical point and that is to be identified with $\hat{A}_{2k, 2k}$ theory. In the $k=2$ case, we derive a system of two ODEs for the scaling functions to the free energy, the time variable being the scaled total mass and make a consistency check on the spectral curve on this matrix model. Comment: 15 pages |
| Databáze: | OpenAIRE |
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